Gyros have been used to measure rotation rates or changes in angular velocity about an axis of rotation. A basic conventional fiber optic gyro (FOG) includes a light source, a beam generating device, and a coil of optical fiber coupled to the beam generating device that encircles an area. The beam generating device transmits light beams into the coil that propagate in a clockwise (CW) direction and a counter-clockwise (CCW) direction along the core of the optical fiber. Many FOGs utilize glass-based optical fibers that conduct light along a solid glass core of the fiber. The two counter-propagating (e.g., CW and CCW) beams experience different pathlengths while propagating around a rotating closed optical path, and the difference in the two pathlengths is proportional to the rotational rate.
In a resonator fiber optic gyro (RFOG), the counter-propagating light beams are desirably monochromatic (e.g., in a single frequency) and circulate through multiple turns of the fiber optic coil and for multiple passes through the coil using a device that redirects light, that has passed through the coil, back into the coil again (i.e., circulates the light), such as a fiber coupler. The beam generating device modulates and/or shifts the frequencies of each of the counter-propagating light beams so that the resonance frequencies of the resonant coil may be observed. The resonance frequencies for each of the CW and CCW paths through the coil are based on a constructive interference condition such that all light-waves, having traversed the coil a different number of times, interfere constructively at any point in the coil. As a result of this constructive interference, an optical wave having a wavelength λ is referred to as “on resonance” when the round trip resonator optical pathlength is equal to an integral number of wavelengths. A rotation of the coil produces a different optical pathlength for clockwise and counterclockwise propagation, thus producing a shift between the respective resonance frequencies of the resonator, and the frequency difference, such as may be measured by tuning the difference in the CW beam and CCW beam frequencies to match the resonance frequency shift of the closed optical path due to rotation, indicates the rotation rate.
In the RFOG, the glass material of the optical fiber may give rise to effects that shift the resonance frequencies of the CW and CCW paths and thus produce a false indication of rotation or inaccurate measurement of rotation rate. Anomalies, stemming from the glass medium, that decrease the accuracy of the rotational rate measurement may be generated from a non-linear Kerr effect, stimulated Brillouin scattering, polarization errors, and Rayleigh backscatter errors. These error mechanisms are also sensitive to the environment which, for example, gives rise to unwanted temperature sensitivity. A reflective mirror may be used to circulate the counter-propagating light beams in the coil multiple times, but this typically reduces the signal-to-noise ratio from losses generated at the transition from the mirror to the coil.
The non-linear Kerr effect occurs when high monochromatic light power inside the RFOG alters the index of refraction of the glass in the optical fiber. A mismatch of intensities of the CW and CCW beams may induce a bias on the observed frequency shifts on the order of several degrees/hour, for example. Stimulated Brillouin scattering (SBS) occurs when high intensity light associated with a high finesse in the fiber resonator causes lasing or stimulated emission in the glass fiber, and this generally promotes large instabilities in the measurement of the resonance frequencies. Polarization-induced errors may result from fiber couplers that incidentally couple light into a second polarization mode, either from one optical fiber to an adjacent optical fiber or within the same fiber. The second polarization mode may resonate producing an asymmetry in the resonance lineshape of the polarization mode used to measure a rotation. Even though the frequency of the second polarization mode is the same for the CW and CCW beams, the amplitude may be different, thus causing different observations, beyond those affected by rotation, of the resonance frequencies of the CW and CCW beams. Polarization-induced errors may severely limit the accuracy of the RFOG because determination of the resonance centers for each of the resonance frequencies of the CW and CCW beams directly affects the rotational rate measurement. Rayleigh backscatter errors may be a source of drift rate in a resonator gyro. Backscattered light from the glass within the fiber or from imperfections with the fiber can interfere with the circulating light beams and cause significant drift rate errors.
The RFOG may encounter additional anomalies that decrease the accuracy of the rotational rate measurement. In a reflecting mode, the ring resonator reflects a portion of light having a state matched with a pre-determined state of the resonator. The portion of light in this desired state, that is the reflected portion, grows as its frequency is detuned from the resonance frequency of the resonator. At resonance, the reflected portion is minimized, thus the resonance frequencies for each of the CW and CCW paths through the fiber optic coil are detected by monitoring the light that does not enter the resonator. The resonance is thus observed as a “resonance dip” because less light is observed when the resonator is near resonance than when the resonator is not near resonance. As previously mentioned, successive recirculation of each of the counter-propagating light beams produces constructive interference at the resonance frequencies, and the center of a resonance dip in the resonance lineshape indicates a resonance frequency. It is desirable to have a definitive symmetrical resonance dip to more accurately indicate the resonance frequency. To this end, the resonator may be designed to circulate light in a pre-determined state (e.g., TEM00-S representing a state of the light having a lowest order spatial mode and a vertical polarization in a free space resonator).
In particular, the total light wave in the matched state (e.g., a mode-matched reflected wave) that is reflected from the resonator comprises two electric field waves, one that is immediately reflected from the mirror or coupler at the entrance to the resonator (e.g., a mode-matched zero-pass wave) and one that is derived from light that has circulated within the resonator (e.g., a mode-matched circulated wave). The mode-matched circulated includes light that has traveled in the resonator coil and has been transmitted back out of the resonator entrance (e.g., via a fiber coupler or mirror). The mode-matched circulated wave amplitude is typically a fraction of the light wave amplitude that circulates within the coil. This fraction is determined by the transmission coefficient of the coupler or mirror. The net result is that the electric field of the total light wave in the matched state is a superposition of the mode-matched zero-pass wave and the mode-matched circulated wave. The intensity of the total mode-matched reflected wave may be determined by the interference between the mode-matched zero-pass wave and the mode-matched circulated wave, which is the subject of detection.
When the frequency of the input wave is substantially detuned from resonance, the mode-matched circulated wave amplitude is substantially zero because the amplitude of the wave from which the mode-matched circulated wave was derived is substantially zero. Thus, the light reflected from the resonator consists of only the mode-matched zero-pass wave, and thus the total mode-matched circulated wave has a maximum intensity. This is true since the mode-matched circulated wave does not interfere destructively with the mode-matched zero-pass wave. Near resonance, the light circulating inside the resonator grows significantly, and thus the light in the mode-matched circulated wave similarly grows significantly and subsequently destructively interferes with the mode-matched zero-pass wave to produce the dip observed in the total mode-matched reflected wave. Further, at the resonance center, the light circulating inside the resonator is at a maximum, and thus the light in the mode-matched circulated wave is at a maximum which produces a maximum destructive interference with the mode-matched zero-pass wave to produce the bottom of the observed dip in the total mode-matched reflected wave. In this ideal case, the resonance dip of the light in the mode-matched state alone is symmetrical. In other words, detuning the input frequency slightly to either side of the dip produces a proportional increase in the intensity of the total mode-matched reflected wave intensity. In practice, a symmetric line-shape is generally required for accurate measurements of the resonance center.
Light energy that is solely in the matched state, or solely in the desired input light component, produces a symmetric resonance dip that is ideal for rotation sensing. However, practical issues may constrain the light energy at the input to the resonator from being substantially in the mode-matched state. For example, some non-resonant, stray, undesired light (e.g., light that is not properly matched in the polarization mode or the spatial mode of the resonator) in the input wave may be present which may be reflected from the resonator and interfere with the light in the total mode-matched reflected state described above. This additional component of light, by interfering with the desired light, may produce an asymmetrical resonance dip, thus producing errors in the detection of the resonance centers. Thus, the symmetry of the resonance dip may be affected by several factors including, but not necessarily limited to, a residual launch light component in the input light beam to the resonator having either 1) an undesired polarization state or 2) light, from the input light beam to the resonator with a spatial distribution that overlaps with higher order spatial modes of the light in the resonator. Both of these typically result from an imperfect input light condition or launch condition at the input to the resonator. Although the residual launch light component may not resonate in the resonator when the desired light component is near resonance, this residual light may adversely affect the observed shape of the resonance dip resulting from the desired light component.
A mode of the resonator refers to a particular electric field transverse electric field distribution and polarization state that reproduces itself at each longitudinal point (e.g., along the axis of propagation) in the resonator after each round-trip through the resonator when at resonance. Because the resonator normally includes both free space optics and a fiber optic waveguide, the modes of the resonator are based on light propagation properties in both media, but the spatial distribution of the resonator mode at points within the fiber is typically a spatial mode of the fiber, or generally, a superposition of modes of the fiber. The preferred case, for the lowest loss and greatest performance, at points along the axis of the fiber, the spatial distribution of the resonator mode is substantially that of the lowest order spatial mode of the fiber (e.g., one that preserves itself while propagating along the length of the fiber).
In addition to the interference from non-resonant residual light components in the launch condition, higher order spatial modes of light in the resonator may resonate or be near resonance and may alter the apparent shape of the resonance dip for the mode used for rotation sensing. For example, resonance of the higher order spatial modes of light may produce additional dips close to the resonance lineshape of the desired mode used for rotation sensing. Additionally, the second polarization state may also resonate or be near resonance and may alter the shape of the resonance dip for the other polarization mode used for rotation sensing. When these additional dips are positioned in proximity to the resonance dips associated with the resonance frequency or superimposed onto the resonance dips associated with the resonance frequency, the observed shape of the resonance dip associated with the resonance frequency may be altered. As previously mentioned, without exciting a resonance, input light that is not properly matched in the polarization mode or the spatial mode of the resonator may distort the shape of the resonance dip of the mode used for rotation sensing.
Interference from non-mode matched residual light in the launch condition having either the undesired polarization state or higher order spatial mode components of the resonator may complicate identification of the resonance centers and provide inaccurate determinations of resonance frequencies and rotations rates. Determination of the resonance centers for each of the resonance frequencies of the CW and CCW beams directly affects the rotational rate measurement and, thereby severely limits the accuracy of the RFOG.
Several mechanisms can produce imperfections in the input light polarization state, thereby producing a component of stray light at the resonator entrance that is not mode-matched. This may result from a wander of the light source polarization state or by a cross-coupling of light due to birefringence in optical elements used to direct light to the resonator entrance. The preferred state inside the resonator may not be exactly known because light inside the resonator may couple to another polarization state such that the preferred state slightly deviates from the intended state. At times, even accurate control of the input state may produce some light in a non-mode-matched condition because this light may not exactly match the light of the resonator mode. Several mechanisms may couple light into the undesired polarization state within the fiber optic resonator to produce a deviation in the intended state. Light may be cross-coupled inside the recirculating device, such as a fiber coupler or within the coil itself. Light may also excite the second polarization state, or couple into the second polarization state, of the resonator when undesirably injected into the optical fiber with a component of the light in the undesired polarization state. This may be exacerbated by possible variances in the states of polarization of the fiber inside the resonator due to temperature or stress variation, thereby making repeated light launches into one polarization state of the resonator more difficult. Even if the light beams are originally introduced to the coil of the RFOG in the first polarization mode, the optical fiber may have one or more imperfections that couple light into the second polarization mode.
In addition to encountering error mechanisms that may affect accuracy, the conventional RFOG may be cost prohibitive for high volume production, particularly for a smaller scale RFOG. The conventional RFOG is an assembly of multiple discrete components (e.g., light source, beam generator, coil, etc.) that has an associated cost for each component and for assembling such components. For smaller scale applications, the cost associated with assembling the RFOG generally increases with the increased cost for miniaturizing each discrete component and aligning the miniaturized discrete optical components.
Accordingly, it is desirable to provide a resonator gyro for small-sized navigation grade applications that attenuates resonance asymmetry errors. In addition, it is desirable to provide a method for attenuating resonance asymmetry errors in a resonator gyro while minimizing inaccuracies due to non-linear Kerr effect, stimulated Brillouin scattering, polarization errors, and bend losses associated with fiber resonator gyros based on conventional optical fiber. Furthermore, other desirable features and characteristics of the present invention will become apparent from the subsequent detailed description of the invention and the appended claims, taken in conjunction with the accompanying drawings and this background of the invention.